Probability distribution

results that are almost certain. The Law of Large Numbers is “A law expressing the fact that if a trial in which all outcomes are independent of each other and equally likely is repeated, then the relative frequency of each outcome approximates its probability with increasing accuracy as the number of repetitions becomes sufficiently large” is the definition given for law of large numbers (Law of Large Numbers). The application of weak law of large…

In the book “the Signal and the noise”, author Nate Silver talks about prediction from many different angles. Silver explains how prediction is a part of our everyday life and how it affects us. From math to history, inside of a class room or on a court/field, prediction is something we deal with on a day to day basis unconsciously. Silver talks about the benefits of failure and how failure is helpful in the long run with making predictions. Throughout the years we have made progress with…

The Randomness of the Universe In the movie, Match Point, directed by Woody Allen, the scales of fate and justice in society are determined by the mere uncertainties of the universe, in other words, by random chance. Chance is the random occurrences that people experience every day, and is a result of entropy. Based on the second law of thermodynamics, the universe has a tendency to move towards disorder or a randomness. This characteristic of entropy can explain how fate is actually an…

Assuming that the target is randomly located in the space at the position which are independent and identically distributed random variables with joint probability density function where Since the space is divided into identical cubic cells with knowing side length then the target is equally probably in each cell and has the probability see Fig. (2). Here, the searching process is assumed to be continuous in both time and space. Also, let are complete revolutions of the spiral with…

is an assumption for financial institutions to process which is known as time aggregation associate with σ in equation 1.3.1. It is related to the risk horizon one would like to generate from a given sample data. For i.i.d(independent identical distribution) returns, based on the statistical knowledge (Jorion:1997), the measurement to forecast the parameter in equation 1.3.1 is, μ=μ_(unit period)*T Equation 1.4 σ=σ_(unit period)*√T Equation 1.5 and for correlated…

are correlated. Regression is better suited for studying functional dependencies between factors. It creates an equation where in if one variable is known, the other can be estimated. Nonparametric tests No assumptions are made about the data distribution. Ordinal properties of data are used instead of absolute data values. Statistical significance with a nonparametric test is difficult to be…

s: Translations are the process of moving around all of the coordinates that make up a shape. All the points move the same distance in the same direction. The transformation is isometric which means that it does not change in shape or sides. If the pre-image moves either right or up the coordination would be adding. If the pre-image moves either left or down the image would be subtraction. The picture to the right is an example of translation. The answer to the question at the bottom would be…

The general model introduced in Fig.4.10 is commonly used to design stable high-order modulators. If a chain of integrators is used to form the loop filter, two main modulators typologies exist [1, 5, 8]: a cascade of M delaying integrators is used to form the filter, where the feedback and the input signals are being fed to each integrator input with different weight factors a_i and b_i (Fig.4.11). The transfer function of the signal filter, L_0, is: while the feedback filter L_1 can be…

One of the many questions posed by those searching for answers on Just Noticeable Difference was if JND could be a suitable as a unit of measure. Analyzing data from two prior experiments, where participants were to discriminate different colors when shown different brightness intervals and applying it to sound also. Once all the data was analyzed, the researchers determined that JND could not be used as a unit of measure (Newman, 1933). Although JND could not be used as a unit of measurement,…

1992). It is a further development and variant of prospect theory. The difference between this version and the original version of prospect theory is that weighting is applied to the cumulative probability distribution function, as in rank-dependent expected utility theory but not applied to the probabilities of individual outcomes The Cumulative Functional A risky prospect f is a function that maps states of the world sS into consequences xX. Outcomes of prospects are arranged in…